有限元法求解瞬态温度场时的数值振荡研究

刘文胜; 李璇; 马运柱; 杨肃

doi:10.21656/1000-0887.380166

有限元法求解瞬态温度场时的数值振荡研究

doi: 10.21656/1000-0887.380166

中南大学(粉末冶金国家重点实验室), 长沙 410083

基金项目: 国家高技术研究发展计划(863计划)(2009AA034300)

详细信息

作者简介:
刘文胜（1967—），男，教授，博士生导师;马运柱（1975—），男，教授，博士生导师（通讯作者. E-mail: yangsupm@csu.edu.cn）.

中图分类号: TK124
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- 被引次数: 0
出版历程
- 收稿日期: 2017-06-13
- 修回日期: 2017-09-25
- 刊出日期: 2018-04-15

Study of Numerical Oscillation in Solving Transient Temperature Fields With the Finite Element Method

Central South University (State Key Laboratory of Powder Metallurgy), Changsha 410083, P.R.China

Funds: The National High-tech R&D Program of China (863 Program) (2009AA034300)

摘要

摘要: 针对有限元求解瞬态温度场时解的振荡问题，通过对热传导矩阵和热容矩阵的分析，研究了数值仿真中解的振荡原因以及消除振荡的方法.研究结果表明，热传导矩阵违反了热力学第二定律以及在迭代初期，协调热容矩阵的单元内温度变化率的连续性假设与实际偏差很大是产生数值振荡的原因.规范单元形状和采用适当的集中热容矩阵，可以有效消除数值振荡.同时，以无限大平板传热过程为背景，通过不同计算方法的对比，验证分析了结论.
- 瞬态温度场 /
- 有限元 /
- 振荡 /
- 热力学第二定律 /
- 集中热容矩阵
Abstract: To overcome the numerical oscillation in solving transient temperature fields with the finite element method, the heat conduction matrix and the heat capacity matrix were analyzed, and the cause for the oscillation of numerical solution as well as the method of eliminating oscillation were studied. According to the results, the cause for the numerical oscillation is that the thermal conduction matrix violates the second law of thermodynamics, and at the beginning of the iteration, the continuity hypothesis of the temperature change rate of the elements in the heat capacity matrix is far from the actual situation. Regularization of element shapes and application of appropriate lumped mass heat capacity matrices can effectively eliminate the numerical oscillation. With an infinite plate in the heat transfer process as an example, the conclusion was verified through comparison between different calculation methods.
- transient temperature field /
- finite element /
- oscillation /
- second law of thermodynamics /
- lumped mass heat capacity matrix

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参考文献(15)

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有限元法求解瞬态温度场时的数值振荡研究

doi: 10.21656/1000-0887.380166

作者简介:
刘文胜（1967—），男，教授，博士生导师;马运柱（1975—），男，教授，博士生导师（通讯作者. E-mail: yangsupm@csu.edu.cn）.

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Study of Numerical Oscillation in Solving Transient Temperature Fields With the Finite Element Method

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留言板

有限元法求解瞬态温度场时的数值振荡研究

doi: 10.21656/1000-0887.380166

作者简介: 刘文胜（1967—），男，教授，博士生导师;马运柱（1975—），男，教授，博士生导师（通讯作者. E-mail: yangsupm@csu.edu.cn）.

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出版历程

Study of Numerical Oscillation in Solving Transient Temperature Fields With the Finite Element Method

计量

出版历程

目录

作者简介:
刘文胜（1967—），男，教授，博士生导师;马运柱（1975—），男，教授，博士生导师（通讯作者. E-mail: yangsupm@csu.edu.cn）.